High-pressure structural parameters of the superconductors $\mathrm{Ce}M{\mathrm{In}}_5$ and $\mathrm{Pu}M{\mathrm{Ga}}_5$ ($M=\mathrm{Co}$,Rh)

High-pressure, angular-dispersive, x-ray diffraction measurements have been performed on “115” superconductors $\mathrm{Ce}M{\mathrm{In}}_5$ and $\mathrm{Pu}M{\mathrm{Ga}}_5$ for $M=\mathrm{Co}$ and Rh. The principal results are of the pressure-dependence of the ratio of the tetragonal lattice parameters, $c∕a$, in each system, which are presented for the purpose of understanding the role that this parameter plays in controlling the value of the superconducting temperature $T_c$. In none of the systems investigated does $c∕a$ scale linearly with the value of $T_c$ under pressure, suggesting that it is not the main parameter to control $T_c$. Values of bulk modulus determined from these measurements are also presented.

Figure 1

Experimentally [by high-$P$ resistivity (Refs. 4, 12)] determined trends in $T_c\left(P\right)$ for ${\mathrm{CeCoIn}}_5$, ${\mathrm{CeRhIn}}_5$, ${\mathrm{PuCoGa}}_5$, and ${\mathrm{PuRhGa}}_5$ (only the smooth “guide-to-the-eye” curves (dotted lines) taken through the data points in Refs. 4, 12 and not the points themselves are shown). The additional $y$ scales on the right-hand side (RHS) of each panel give the “anticipated” $c∕a$ ratio, expected if $T_c$ scaled (linearly) with $c∕a$ under pressure. The temperature scales [left-hand side (LHS)] are such that the total range of $c∕a$ is approximately the same for each panel $(\approx 0.025)$.

Figure 2

Examples of (area detector) diffraction patterns for Ce (left image) and Pu (right image) 115 compounds. The Ce data are from the ${\mathrm{CeRhIn}}_5$ run using ${\mathrm{N}}_2$ (PTM), and the Pu data are from ${\mathrm{PuCoGa}}_5$ (PTM: oil). Both data sets are representative of the typical data from each family (i.e., smooth rings for Ce-115’s and spotty rings for Pu-115’s), however, the use of a longer x-ray wavelength in ${\mathrm{PuRhGa}}_5$ study implied that a smaller (total) number of rings was collected.

Figure 3

Examples of diffraction patterns (after integration of area detector data) and fits for Ce (left panel) and Pu (right panel) 115 compounds, at various pressure values. The fits (solid lines through data points) are by profile matching. Reflection positions (vertical bars) and difference curves are also shown; the (001) position, for each pattern, is that of lowest $2\theta$ vertical bar. The weak reflection labeled by an asterisk (Ce-115 patterns) is due to excess In flux. The Ce-115 data is from ${\mathrm{CeRhIn}}_5$ with ${\mathrm{N}}_2$ as PTM, and the Pu-115 data is from ${\mathrm{PuCoGa}}_5$ (PTM: oil).

Figure 4

Normalized unit-cell volume $(V∕V_0)$ as a function of pressure for $\mathrm{Ce}M{\mathrm{In}}_5$: (a) $M=\mathrm{Co}$ and (b) $M=\mathrm{Rh}$. In (a) open points (circles and diamonds) distinguish two runs [ours and one performed by Méasson et al. (Ref. 15), respectively] which used the same type of PTM (oil). In (b) open points are for a run with ${\mathrm{N}}_2$ as PTM, and closed points are with oil. The solid lines are fits to a Birch-Murnaghan equation of state, with the corresponding $B_0$ and $B_0^{\prime }$ values given [errors on these values refer to the least significant digit(s)]. Errors on the pressure variable and relative volumes are smaller than the plotting points.

Figure 5

Normalized unit-cell volume $(V∕V_0)$ as a function of pressure for $\mathrm{Pu}M{\mathrm{Ga}}_5$: (a) $M=\mathrm{Co}$ and (b) $M=\mathrm{Rh}$. In both (a) and (b), the solid lines are Birch-Murnaghan fits made to the data in the range $P<10\mathrm{GPa}$. Values of $B_0$ and $B_0^{\prime }$ [with errors to the least significant digit(s)] corresponding to each fit are given [in (b) $B_0^{\prime }$ was fixed]. Errors on the pressure variable and relative volume are smaller than the plotting points.

Figure 6

Normalized lattice parameters $a_{\mathrm{rel}}$ and $c_{\mathrm{rel}}$ in ${\mathrm{PuCoGa}}_5$ as a function of pressure (the values have been normalized to unity at the starting pressure of 0.7 GPa), showing an anomaly in $c$ in the range 10–14 GPa due to PTM freezing. The values were obtained by (a) an analysis of the entire diffraction pattern and (b) ($c$ lattice parameter only) an analysis of a single diffraction spot. The upper inset in (b) shows the relevant “spot” [from the (001) ring] at 0.7 GPa. Here the arrow points in the direction of increasing $2\theta$; the spot is located just below this arrow. The lower inset shows the profile of the spot along the $2\theta$ direction, fitted to a Voigt function. Errors on lattice parameters in (a) and (b) are smaller than the plotting points.

Figure 7

$c∕a$ as a function of pressure in ${\mathrm{CeRhIn}}_5$: (a) from this study (circles) and (b) from the Kumar et al. study (Ref. 14) (squares). In each panel, closed and open points distinguish data from runs using different PTMs; for our data, closed are for oil and open for ${\mathrm{N}}_2$. The solid line (guide-to-the-eye) curve through our data in (a) is reproduced in (b) [where it appears “flatter” due to the $(4\times )$ larger $y$-scale range of the lower panel]. The dashed line curve in (b) is the trend Kumar et al. conclude from their data.

Figure 8

$c∕a$ as a function of pressure in ${\mathrm{CeCoIn}}_5$: (a) from this study (circles) and (b) from the Kumar et al. study (Ref. 6) (squares). In (a) the results from a study by Méasson et al. (Ref. 15) are also shown (open diamonds; $P<4.2\mathrm{GPa}$). The solid line (guide-to-the-eye) curve through our data in (a) is reproduced in (b) (the sizes of $y$-scale ranges are identical in the two panels). The dashed line in (b) is the trend Kumar et al. conclude from their data.

Figure 9

$c∕a$ as a function of pressure in $\mathrm{Pu}M{\mathrm{Ga}}_5$ ($M=\mathrm{Co}$,Rh). The solid line (guide-to-the-eye) curves neglect the points in the range $10\mathrm{GPa}<P<14\mathrm{GPa}$, for the reason explained in the text.

Figure 10

Summary of results: experimentally determined trends (solid lines) in $c∕a$ as a function of pressure for all the compounds investigated in this study compared to the anticipated trends from Fig. 1 (dotted lines). For the Ce-115 compounds, the trends in $c∕a\left(\mathrm{P}\right)$ derived experimentally by Kumar et al. (Refs. 14, 6) are also shown (dashed lines).